The value 5,200 in the function f(x) = 5,200(1.1)^x represents the initial population of cottontail rabbits in Orange County. This is because in the context of population modeling, the initial population refers to the starting population size before any growth or decline occurs.
In this case, the function f(x) = 5,200(1.1)^x models the yearly growth of the cottontail rabbit population. The value 5,200 represents the initial population of rabbits in Orange County before any growth takes place. As x (the number of years) increases, the population grows at a rate of 10% per year (as indicated by the growth factor 1.1).
Therefore, in the given function:
- The growth factor is 1.1, which represents a 10% increase in population each year.
- The growth rate is not explicitly provided in the function but can be calculated as 10% based on the growth factor.
- The number of years is represented by the variable x in the function, indicating the time over which the population grows.
- The value 5,200 specifically denotes the initial population of cottontail rabbits in Orange County.
Understanding the significance of each component in the function helps in interpreting the role of 5,200 as the initial population accurately.
